Mathematics 10 — Exercise 3.4 · Q1 (ii) AB

Full question

Find AB, if possible.

Step-by-step solution

1. 2 columns in the first matrix match 2 rows in the second. The product has 1 rows and 1 columns.

   $$(\left[\begin{array}{cc}1& -2\end{array}\right],\left[\begin{array}{c}3\\ -4\end{array}\right])$$

2. Calculate this operation before combining the remaining terms.

   $$\left(-1\right)\times \left(-8\right)=8$$

3. Entry (1,1): pair row 1 with column 1 and add their products.

   $$1\times 3--8$$

4. Calculate this individual product, including its signs.

   $$1\times 3=3$$

5. Calculate this individual product, including its signs.

   $$\left(-2\right)\times \left(-4\right)=8$$

6. Add the calculated products to obtain this entry.

   $$3+8=11$$

7. Place the calculated entries in their original row and column positions.

   $$\left[\begin{array}{c}11\end{array}\right]$$

Answer

The final answer is shown below.